The generator matrix

 1  0  0  0  1  1  1  1 2X+2  1 X+2  1  0  1 2X+2  1 2X+2  1 3X 3X+2  1  1  1  1 2X 3X  1  1  X 2X+2  1  1 2X+2  1  1  1  1 3X 3X+2  1  X 3X+2  2 3X 3X+2  1 2X+2  1 2X  1  0  1  X  1  1  1  1 2X 2X+2  0  1  1 X+2 2X+2  0  1  1  2  2  1
 0  1  0  0  X 2X+3 2X+1  2  1 X+3  1 3X+2  1 X+1 3X+2 X+1  1 3X+2  1  1 3X+2 X+2 2X+2 2X+1  2 X+2 X+1 2X+1 3X  1 3X+1 3X+3  1  2  2 2X+2 3X+1 2X+2  0  X  1  1 2X+2  0  1 3X+2  1 3X+2  0  1  1 2X+1 3X+2  1 3X+2 2X+1  X  1  X  X 3X  1 3X 3X+2  1 X+1 2X+3 2X X+2 2X
 0  0  1  0  0 2X+2  1 2X+3 2X+3 2X  0 3X+3 3X+1  1  1 2X 3X+2  2 3X+2 3X+1 3X 2X+3  1 X+2  1  1  3 X+3 3X 3X+1 3X+2 3X+3 3X  X 2X+1 X+3 2X 3X+2  1  X 2X+1  2 2X  1 3X+1 2X 2X 3X+3  1 3X 2X+1 2X+3  1 3X+3  2 2X 2X+1  2  1  1 3X+1 3X  1  1  3  1 2X+1  X  1 2X
 0  0  0  1  1 3X+3 2X+2 X+1 3X+3 3X X+1 X+2  X X+1  1 X+3 2X+1 X+3 3X+2 2X+2 2X 3X  3 3X+2  3 2X 2X+3  0  1  3  1  3 3X+3  1  X X+3 2X  1  X  3 X+1 2X  1  3  0 X+2  3 3X+3  3 2X+3 X+1  3 3X X+2 2X+2  0 3X+1 X+3 X+2  2 2X+1  1 3X+2 2X+1  0  X  2  1  2 2X
 0  0  0  0 2X+2  0  0  0  0 2X+2 2X+2 2X+2  2 2X+2  2  2 2X 2X 2X+2  0  2 2X 2X+2  0 2X 2X+2  2  2  2 2X+2 2X+2 2X 2X+2  0  2 2X 2X+2 2X 2X+2 2X  0 2X  2  0 2X+2  2 2X  0  2 2X  2  0  2  2  0 2X+2  2 2X  0  2 2X  2 2X+2  0 2X+2  0  2  0  0 2X

generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+92x^61+889x^62+2180x^63+5289x^64+8476x^65+14694x^66+20162x^67+28952x^68+31666x^69+36563x^70+32066x^71+29992x^72+20698x^73+14571x^74+7764x^75+4588x^76+1822x^77+986x^78+430x^79+134x^80+54x^81+35x^82+22x^83+4x^84+6x^85+6x^86+2x^93

The gray image is a code over GF(2) with n=560, k=18 and d=244.
This code was found by Heurico 1.16 in 654 seconds.